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Question 1199626: How does the graph of the hyperbola whose equation is (y2)/4 - (x2)/9 = 1 open?
A. A hyperbola does not open.
B. Hyperbola opens to the sides.
C. Hyperbola opens toward its vertices.
D. This graph is not a hyperbola.
E. Hyperbola opens toward its center.
F. Hyperbola opens up and down.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52792)   (Show Source):
You can put this solution on YOUR website! .
Make a sketch - and you will see.
Option (F)
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It is a fortune that there are only 6 options in the list.
Would the number of options be 26 or 46, the problem could be much harder.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Note for future reference: It is standard to use "^" (shift-6) to represent exponentiation. The equation in your problem is (y^2)/4 - (x^2)/9 = 1.
The equation has both x^2 and y^2 terms, with opposite signs, and it contains no xy term. So the graph is a hyperbola that opens either right and left (option B -- "to the sides") or up and down (option F).
We need to determine which of those options is the right one.
In my experience, a lot of references teach a rule: if the x^2 term is positive, the hyperbola opens in the x direction (right and left); if the y^2 term is positive, the hyperbola opens in the y direction (up and down).
That works... but if a student just memorizes a rule and then forgets the rule or gets confused about what the rule says, then he will have trouble finding the answer.
I recommend using a method that uses logical reasoning rather than memorization.
What I do when I see your equation is suppose that y=0; then the equation says  , which makes x^2 negative, which is impossible. That means y can't be zero -- and that means the hyperbola opens up and down.
Using logical reasoning rather than a memorized rule helps the student UNDERSTAND why the graph opens in the direction it does; and that makes the student enjoy the math more.
ANSWER: up and down -- option F
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